Transit Authority president Larry Reuter vowed yesterday to improve service on the crowded Lexington Avenue line as the battle rages over building a Second Avenue subway.

But some measures will take at least three years to install on the only line that runs up and down the East Side – such as a new system to more precisely track trains.

Riders vexed by the Lex said they want relief from crowded trains – now.

They tell horror stories that Lex trains and station platforms are so jammed that they can’t get on or off trains in rush hour. One rider told The Post she nearly got crushed after slipping between the platform and train.

But Reuter said new subway cars that will hit the rails over the next few years will have wider doors, thus making it easier for passengers to board the 4, 5 and 6 trains.

That, in turn, will speed up trains by cutting down the time it takes for riders to get in and out of crowded cars, he said.

During rush hour, a maximum of 26 or 27 rush-hour trains pass through each Lexington track. Reuter said he wants to increase that to 30 trains – or one every two minutes.

The TA will also increase the number of platform conductors and supervisors at stations to control crowds and improve safety. There are about a dozen transit employees who now monitor the platforms at Grand Central station.

The agency also intends to increase “step aside” public-address announcements to remind passengers to let others first get off trains before boarding, and install more closed-circuit monitors that would assist conductors to see when car doors are clear.

Reuter said a new centralized computer train-tracking system – called Automatic Train Supervision – will replace the antiquated communication unit and help increase the number of rush-hour trains.

“That allows us to know where the trains are on the Lexington line. We don’t know that now except by radio and telephone messages back and forth” with train crews, he said. But the train-tracking system won’t be in place until 2003-2004.